Quotients of primes in an algebraic number ring
- MathematicsNotes on Number Theory and Discrete Mathematics
It has been established on many occasions that the set of quotients of prime numbers is dense in the set of positive real numbers. More recently, it has been proved that the set of quotients of…
On some new arithmetic functions involving prime divisors and perfect powers
- MathematicsElectron. Notes Discret. Math.
Survey of Dirichlet Series of Multiplicative Arithmetic Functions
The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is…
Undecidable and decidable restrictions of Hilbert's Tenth Problem: images of polynomials vs. images of exponential functions
- Mathematics, ChemistryMath. Log. Q.
It is shown that restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section.
Quotients of Primes in a Quadratic Number Ring
It has been established on many occasions that the set of quotients of prime numbers is dense in the set of positive real numbers. More recently, it has been proved in the Monthly that the set of…
Binary quadratic forms, elliptic curves and Schoof's algorithm
- Computer Science, Mathematics
In this thesis, I show that the representation of prime integers by reduced binary quadratic forms of given discriminant can be obtained in polynomial complexity using Schoof's algorithm for counting…
NOTES ON ESPECIAL CONTINUED FRACTION EXPANSIONS AND REAL QUADRATIC NUMBER FIELDS
The primary purpose of this paper is to classify real quadratic fields Q(√d) which include the form of specific continued fraction expansion of integral basis element 𝑤𝑑 for arbitrary period length…
New Results on Primes from an Old Proof of Euler's
In 1737 Leonard Euler gave what we often now think of as a new proof, based on infinite series, of Euclid's theorem that there are infinitely many prime numbers. Our short paper uses a simple…